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222-9+11+12:2*14+14 = ? ( )

Toán Lớp 9: A=[1/(√x-1) – 1/√x]:[(√x+1)/(√x-2) -(√x+2)/(√x-1)] Rút gọn A

Tháng Tư 24, 2022 Toán học 2 Comments 0 views

Toán Lớp 9: A=[1/(√x-1) – 1/√x]:[(√x+1)/(√x-2) -(√x+2)/(√x-1)]
Rút gọn A

Comments ( 2 )

  1. truongankimtrong
    truongankimtrong
    24 Tháng Tư, 2022 at 11:22 sáng
    Reply
    A = [ 1/(\sqrt{x}-1) – 1/(\sqrt{x}) ] : [ (\sqrt{x}+1)/(\sqrt{x}-2) – (\sqrt{x}+2)/(\sqrt{x}-1) ]
    =  ( \sqrt{x} – (\sqrt{x}-1))/(\sqrt{x} (\sqrt{x}-1)) : ((\sqrt{x}+1)(\sqrt{x}-1) – (\sqrt{x}+2)(\sqrt{x}-2))/((\sqrt{x}-2)(\sqrt{x}-1))
    =  (\sqrt{x} – \sqrt{x} +1)/(\sqrt{x} (\sqrt{x}-1)) : ( (x-1) – (x-4))/((\sqrt{x}-2)(\sqrt{x}-1))
    = 1/(\sqrt{x}(\sqrt{x}-1)) :  (x – 1 – x+4)/((\sqrt{x}-2)(\sqrt{x}-1))
    =  1/(\sqrt{x} (\sqrt{x}-1)) . ((\sqrt{x}-2)(\sqrt{x}-1))/3
    =  (\sqrt{x}-2)/(3 \sqrt{x})

  2. tonhitruc
    tonhitruc
    24 Tháng Tư, 2022 at 11:22 sáng
    Reply
    Giải đáp:
    ĐKXĐ : x \ne 1; x \ne 4; x >0
    A=(1/(\sqrt{x}-1)-1/(\sqrt{x})):((\sqrt{x}+1)/(\sqrt{x}-2)-(\sqrt{x}+2)/(\sqrt{x}-1))
    =((\sqrt{x})/[\sqrt{x}(\sqrt{x}-1)]-(\sqrt{x}-1)/[\sqrt{x}(sqrt{x}-1)]):([(\sqrt{x}+1)(\sqrt{x}-1)]/[(\sqrt{x}-2)(\sqrt{x}-1)]-[(\sqrt{x}+2)(\sqrt{x}-2)]/[(\sqrt{x}-2)(\sqrt{x}-1)])
    =((\sqrt{x}-\sqrt{x}+1)/[\sqrt{x}(\sqrt{x}-1)]:((x-1-x+4)/[(\sqrt{x}-2)(\sqrt{x}-1)])
    =((1)/[\sqrt{x}(\sqrt{x}-1)]):(3)/[(\sqrt{x}-2)(\sqrt{x}-1)])
    =[(\sqrt{x}-2)(\sqrt{x}-1)]/[\sqrt{x}(\sqrt{x}-1).3]
    =(\sqrt{x}-2)/(3\sqrt{x})

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222-9+11+12:2*14+14 = ? ( )

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